English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper, we focus on the "positive" $l_2$ induced norm of discrete-timelinear time-invariant systems where the input signals are restricted to benonnegative. To cope with the nonnegativity of the input signals, we employcopositive programming as the mathematical tool for the analysis. Then, byapplying an inner approximation to the copositive cone, we derive numericallytractable semidefinite programming problems for the upper and lower boundcomputation of the "positive" $l_2$ induced norm. This norm is typically usefulfor the stability analysis of feedback systems constructed from an LTI systemand nonlinearities where the nonlinear elements provide only nonnegativesignals. As a concrete example, we illustrate the usefulness of the "positive"$l_2$ induced norm for the stability analysis of recurrent neural networks withactivation functions being rectified linear units.

$l_2$ Induced Norm Analysis of Discrete-Time LTI Systems for Nonnegative  Input Signals and Its Application to Stability Analysis of Recurrent Neural  Networks